FPGA Qubit Package 6.111 Final Project...
Transcript of FPGA Qubit Package 6.111 Final Project...
Francisca Vasconcelos and Megan Yamoah
FPGA Qubit Package6.111 Final Project Proposal
equs.mit.eduEngineering Quantum Systems
Engineering Quantum Systems (EQuS) GroupMassachusetts Institute of Technology6 November 2018
Vasconcelos & Yamoah - 26.111 Final Project - Fall 2018
• Implement useful pre-processing for superconducting quantum devices
• Involves:– Processing microwave signals from devices at ~20 mK– Classifying state– Outputting data in a meaningful format
• Why FPGA?– Feedback– Quantum algorithms
Introduction
50 µm
J. Yoder, D. Kim, et al., (2016)
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• Qubit state represented in 2D Hilbert space– Complex number space– Superpositions
• Measurement– Single basis– Wave function collapse– Statistical
• State discrimination
Background
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Lab Equipment
AWG Cryogenic Fridges with Qubit Packages
Lab Measurement RacksKeysight PXI Enclosure
Xilinx Kintex-7with Keysight compatibility
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Broad Block Diagram
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Pre-processing Diagram
Integration
2 x ~100 16 bit values
Counter-rotation
CORDIC Implementation~1096 LUTs, ~1050 FFs
Timing ModuleDetermine when to start taking data
trigger
start
ADC Input:10 x 16 bit
NUM_SAMPLESSAMPLE_FREQ
raw I-Q values2 x 16 bit
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Initial Processing - Background
Qubit output
I-Q mixer output
Complex number representation
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• Iterative algorithm• Represent rotation matrix as multiplication by a power of 2 or adding
operations
CORDIC
COordinate Rotation DIgital Computer
https://www.xilinx.com/support/documentation/ip_documentation/cordic/v6_0/pg105-cordic.pdf
Vector rotation
CORDIC
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Binning / Classification Diagram
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Binner
• Divide I-Q plane into squares (user defines resolution)• Continuously bin values into this 2D histogram• Once measurement is over, report count for each bin • Decreased resolution reduces amount of data sent to computer &
increases processing speed
Actual Data Binned Data(Specifiable # Bins & Bin Width)
Vasconcelos & Yamoah - 116.111 Final Project - Fall 2018
Classification
• Easier: Horizontal (assume I-Q mapping has been rotated) • Harder: Linear with Proposed approach: Geometric Method
(No need to use arctan, sqrt, or any other complicated functions!)
Excited State
Ground State
ae
g
(0,0)
(iE-iL,qE-qL)
I
Q
(iG-iL,qG-qL)
Excited State
Ground State
ae
g
(iL,qL)
(iE,qE)
(iG,qG)
I
QExcited State
Ground State
I
Q
1) Get values to be classified 2) Create vector representation 3) Map vectors to origin
4) Compute dot products and accordingly bin values:
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Megan’s Goals• Baseline
– Receive and output digitized signal values
– Output random I-Q values• Expected
– CORDIC rotation– Integration / Averaging
• Stretch– De-noising– Integrate in lab measurement chain
Goals & Timeline
Fran’s Goals• Baseline
– Data dump– Data read
• Expected– Horizontal classifier– Configuration parameters– Binner– Basic Labber integration
• Stretch– Linear classification – Report classifier distances– Full integration in lab measurement
chain (run QST)
Now 12/12Thanksgiving
Baseline Completed
Work on ExpectedWork on Baseline
Complete Expected
Begin Stretch Work on Stretch Wiggle/Debug Room